The present invention relates generally to optimization, and relates specifically to optimization of print shop facilities.
Production facilities are frequently faced with problems dealing with multiple job scheduling. When production facilities work on several different products requiring variable processing times on different workstations, optimizing production is not a trivial problem. Such optimization problems are often discussed and approached in terms of job sequencing, which can be an NP-hard problem even using simple formulations. Moreover, typical job sequencing can sometimes miss the advantages that derive from working on several products simultaneously.
It is an object of the present invention to determine optimal co-production rates for a plurality of products that lead to better overall productivity. Described herein is a method for analyzing a production facility characterized by various processing rates for jobs involved. The method determines which jobs should be co-produced, if any, and at what rates in order to have a maximum benefit. The method is easy to implement because it involves ordinary linear mathematical programming. Because of the simplicity of the method, it can be used dynamically to account for the current state of facility and jobs. In addition, the method of the present invention can be used to determine if a more involved search for optimal sequencing is worthwhile.
In particular, a method for optimizing a production facility is described herein, where the facility has at least one workstation for producing products. For example, at least of the workstations can be a print shop workstation. The method includes finding a bottleneck rate for each product. The bottleneck rate represents the inverse of a maximum effective processing time of the at least one workstation. The method further includes associating a production rate for each product, and computing optimal production rates by utilizing an objective function of the bottleneck rates and the production rates. The at least one workstation may include processing personnel or operators, and/or at least one machine. For example, the at least one workstation can include a machine for manufacturing image forming systems.
In one embodiment of the present invention, the optimal production rates substantially maximize the objective function subject to capacity constraints of the at least one workstation, and the objective function is a linear function of the inverse of the bottleneck rates, and a linear function of the production rates. For example, the objective function can be a sum of products of the production rates and the inverse of the bottleneck rates. Each product may be associated with an optimal production rate computed by utilizing the objective function and the method may further include manufacturing the products at the optimal production rates associated therewith.
The method described herein may be employed dynamically, so that the optimal production rates are re-calculated to reflect a changing status of the facility and of jobs in the facility. For example, a status of the facility can change because of machine failures and repairs, and a status of jobs can change because of job completions and arrivals of new jobs or because of renegotiated due times. A job can be understood as a requirement to produce a certain amount of a specified product by a specified due time or within a certain amount of time.
Also described herein is a production facility that includes at least one workstation for producing products, each product having a bottleneck rate representing the inverse of a maximum effective processing time of the at least one workstation, and a central processor having instructions to input the bottleneck rate of each product, and to output an optimal production rate for each product. The instructions utilize an objective function of the bottleneck rate of each product to output the optimal production rate for each product. Moreover, the instructions can include a subroutine for maximizing the objective function to obtain the optimal production rate for each product subject to capacity constraints of the at least one workstation.
The optimal production rate output by the central processor can influence a production rate of the at least one workstation. The optimal production rates can influence the at least one workstation by, for example, controlling average release rates of different products on the floor of the facility, as in constant-work-in-process (CONWIP) regulated production. The optimal production rates may also influence the at least one workstation by, for example, giving rise to more detailed instructions involving the order in which products should be processed.
Also described herein is a method for optimizing a production facility that produces Np products using Nw workstations, where Np and Nw are natural numbers. The set of natural numbers is the set of integers greater than zero. The method includes finding a bottleneck rate for each of the Np products. The bottleneck rate for product j, rjb, where j=1,2, . . . , or Np, represents the inverse of a maximum effective processing time of the workstations. The method further includes associating a production rate with each of the Np products, the production rate of product j being denoted by uj, where j=1,2, . . . , or Np, and computing optimal production rates by utilizing an objective function of r1b, r2b, . . . , rNpb, and u1, u2, . . . , UNp.
In one embodiment of the present invention, the objective function is substantially equal to xcexa3juj/rjb, and the optimal production rates substantially maximize the objective function subject to capacity constraints.
Other objective functions can be used. For example, one method of the present invention for optimizing a production facility that produces Np products using Nw workstations, where Np is a whole number greater than one, and Nw is a whole number greater than zero, includes finding a processing time tji associated with product j and workstation i, for j=1, . . . , Np, and i=1, . . . , Nw. The method further includes associating a production rate uj with product j, for j=1,2, . . . , Np, and computing optimal production rates by utilizing an objective function of the processing times and the production rates, such as the function given by Equation (4) below.